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Minimax Problems with Coupled Linear Constraints: Computational Complexity, Duality and Solution Methods
Ioannis Tsaknakis, Mingyi Hong, Shuzhong Zhang
In this work we study a special minimax problem where there are linear constraints that couple both the minimization and maximization decision variables. The problem is a generaliz…
Primal-Dual First-Order Methods for Affinely Constrained Multi-Block Saddle Point Problems
Junyu Zhang, Mengdi Wang, Mingyi Hong +1
We consider the convex-concave saddle point problem , where the decision variables and/or subj…
Decentralized Riemannian Gradient Descent on the Stiefel Manifold
Shixiang Chen, Alfredo Garcia, Mingyi Hong +1
We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a…
A Near-Optimal Algorithm for Stochastic Bilevel Optimization via Double-Momentum
Prashant Khanduri, Siliang Zeng, Mingyi Hong +3
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAI…
On the Local Linear Rate of Consensus on the Stiefel Manifold
Shixiang Chen, Alfredo Garcia, Mingyi Hong +1
We study the convergence properties of Riemannian gradient method for solving the consensus problem (for an undirected connected graph) over the Stiefel manifold. The Stiefel manif…
First-Order Algorithms Without Lipschitz Gradient: A Sequential Local Optimization Approach
Junyu Zhang, Mingyi Hong
First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the…